Why does a gasoline engine run hot on a lean fuel to air mix?

A gasoline engine runs hot on a lean fuel-to-air mix because there is less fuel available to absorb and dissipate heat during combustion. This can lead to higher combustion temperatures, as the excess air increases the oxygen concentration, resulting in more complete and faster combustion. Additionally, the lean mixture can cause parts of the engine, like the cylinder head and exhaust valves, to overheat, potentially leading to pre-ignition or engine knock. Overall, operating on a lean mixture increases thermal stress, which can damage engine components over time.